Phase diagram of the spin quantum Hall transition

We study a system which can be realized in a dirty, gapless superconductor in which time-reversal symmetry for orbital motion is broken, but spin-rotation symmetry is intact. We present a phase diagram in a phase-space of spin Hall conductance ϵ and energy of quasiparticles Δ. It exhibits a direct transition between two insulating phases with quantized Hall conductances of zero and two for the conserved quasiparticles when Δ = 0. The energy of the quasiparticles acts as a relevant symmetry-breaking field at the critical point, which splits the direct transition into two conventional plateau transitions. We use updated correct values of the critical exponents to define these two critical lines as ϵ ∼ ±Δ^6/7.